1RecentProgressintheTheoryofNuclearForces20thInternationalIUPAPConferenceonFew-BodyProblemsinPhysicsAugust20-25,2021,Fukuoka,JapanR.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/12R.MachleidtUniversityofIdahoOutlineThehistoryoftheprogressNuclearforcesfromchiralEFT:BasicideasandcurrentstatusTheopenissuesProperrenormalizationofchiralforcesSub-leadingmany-bodyforcesOutlookR.Machleidt2Prog.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/12R.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/123R.Machleidt42Nforces3Nforces4NforcesLeadingOrderNext-to-Next-toLeadingOrderNext-to-Next-to-Next-toLeadingOrderNext-toLeadingOrderTheHierarchyofNuclearForcesProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/12R.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/1252Nforces3Nforces4NforcesLeadingOrderNext-to-Next-toLeadingOrderNext-to-Next-to-Next-toLeadingOrderNext-toLeadingOrderTheHierarchyofNuclearForcesR.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/126N3LOPotentialbyEntem&Machleidt,PRC68,041001(2003).NNLOandNLOPotentialsbyEpelbaumetal.,Eur.Phys.J.A19,401(2004).R.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/127Thisis,ofcourse,allverynice;Howeverthereisa“hidden〞issueherethatneedsourattention:RenormalizationR.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/128So,what’sthisRenormalizationabout?SeealsocontributionsbyGegelia,Ando,Harada,Kukulin.R.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/129TheEFTapproachisnotjustanotherphenomenology.It’sfieldtheory.Theprobleminallfieldtheoriesaredivergentloopintegrals.Themethodtodealwiththeminfieldtheories:1.Regularizetheintegral(e.g.applya“cutoff〞)tomakeitfinite.2.RemovethecutoffdependencebyRenormalization(“counterterms〞).R.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/1210Forcalculatingpi-piandpi-Nreactionsnoproblem.However,theNNcaseistougher,becauseitinvolvestwokindsof(divergent)loopintegrals.R.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/1211Thefirstkind:“NNPotential〞:irreduciblediagramscalculatedperturbatively.Example:

Countertermsperturbativerenormalization

(orderbyorder)R.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/1212R.Machleidt12Thefirstkind:“NNPotential〞:irreduciblediagramscalculatedperturbatively.Example:

Countertermsperturbativerenormalization

(orderbyorder)Thisisfine.Noproblems.R.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/1213Thesecondkind:ApplicationoftheNNPot.intheSchrodingerorLippmann-Schwinger(LS)equation:non-perturbativesummationofladderdiagrams(infinitesum):

1313Indiagrams:+++…R.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/121414Thesecondkind:ApplicationoftheNNPot.intheSchrodingerorLippmann-Schwinger(LS)equation:non-perturbativesummationofladderdiagrams(infinitesum):Divergentintegral.Regularizeit:Cutoffdependentresults.Renormalizetogetridofthecutoffdependence:

14Non-perturbativerenormalizationR.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/1215R.Machleidt15Thesecondkind:ApplicationoftheNNPot.intheSchrodingerorLippmann-Schwinger(LS)equation:non-perturbativesummationofladderdiagrams(infinitesum):Divergentintegral.Regularizeit:Cutoffdependentresults.Renormalizetogetridofthecutoffdependence:

15Non-perturbativerenormalization15Withwhattorenormalizethistime?Weinberg’ssilentassumption:Thesamecountertermsasbefore.(“Weinbergcounting〞)Thereareseveraloptionsfor

non-perturbativerenormalization.

Iwilldiscusstwoofthem:InfinitecutoffrenoFinitecutoffrenoR.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/1216Inlowerpartialwaves(?shortdistances),ingeneral,noorderbyorderconvergence;dataarenotreproduced.Inperipheralpartialwaves(?longdistances),alwaysgoodconvergenceandreproductionofthedata.Thus,long-rangeinteractiono.k.,short-rangenot(shouldnotbeasurprise:theEFTisdesignedforQ<Λχ).Atallorders,eitherone(ifpot.attractive)orno(ifpot.repulsive)counterterm,perpartialwave:Whatkindofpowercountingschemeisthis?NotWeinbergCounting!

Wherearethesystematicorderbyorderimprovements?R.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/1217Option1:Nonperturbativeinfinite-cutoffrenormalizationuptoN3LOObservationsandproblemsR.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/1218R.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/1219Inlowerpartialwaves(?shortdistances),ingeneral,noorderbyorderconvergence;dataarenotreproduced.Inperipheralpartialwaves(?longdistances),alwaysgoodconvergenceandreproductionofthedata.Thus,long-rangeinteractiono.k.,short-rangenot(shouldnotbeasurprise:theEFTisdesignedforQ<Λχ).Atallorders,eitherone(ifpot.attractive)orno(ifpot.repulsive)counterterm,perpartialwave:Whatkindofpowercountingschemeisthis?NotWeinbergCounting!Wherearethesystematicorderbyorderimprovements?R.Machleidt19Option1:Nonperturbativeinfinite-cutoffrenormalizationuptoN3LOObservationsandproblemsNogood!AndWeinbergCountingfails.Option2:RethinktheproblemfromscratchEFFECTIVEfieldtheoryforQ≤Λχ≈1GeV.So,youhavetoexpectgarbageaboveΛχ.Thegarbagemayevenconverge,butthatdoesn’tmeanit’sproperrenormalization(itmaybe“peratization〞,Epelbaum&Gegelia‘09).So,stayawayfromterritorythatisn’tcoveredbytheEFT.R.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/1220Option2:Nonperturbativeusingfinitecutoffs≤Λχ≈1GeV.

Goal:Find“cutoffindependence〞foracertainfiniterangebelow1GeV.

R.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/1221Veryrecently,asystematicinvestigationofthiskindhasbeenconductedbyusatNLOandNNLOusingWeinbergCounting,i.e.2contactsineachS-wave(usedtoadjustscatt.lengthandeff.range),1contactineachP-wave(usedtoadjustphaseshiftatlowenergy).R.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/1222NotethattherealthingareDATA(notphaseshifts),e.g.,NNcrosssections,etc.Thereforebetter:Lookforcutoffindependenceinthedescriptionofthedata.Notice,however,thattherearemanydata(about6000NNDatabelow350MeV).Therefore,itmakesnosensetolookatsingledatasets(observables).Instead,oneshouldcalculatewithNthenumberofNNdatainacertainenergyrange.R.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/1223Χ2/datumfortheneutron-protondataasfunctionofcutoffinenergyintervalsasdenotedTherearerangesofcutoffindependence(“plateaus〞)R.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/1224Theplateausimprovewithincreasingorder.R.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/1225BestandmostrealisticOption:Nonperturbativeusingfinitecutoffs≤Λχ≈1GeV.Forthis,wehaveshown:

Cutoffindependenceforacertainfiniterangebelow1GeV(shownforNLOandNNLO).Order-by-orderimprovementofthepredictions.ThisiswhatyouwanttoseeinanEFT!

RenormalizationSummaryR.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/1226Chiralthree-nucleonforces(3NF)Onanothertopic:R.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/1227The3NFatNNLO;usedsofar.Prog.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/1228R.MachleidtSeetalksatthisconferencebyBacca,Fonseca,Otsuka,Quaglioni,Sekiguchi,Viviani,Witala;andcontributionsinParallelIIIcandIVcthisafternoon.Medium-massnuclei:Nuclearandneutronmatter:Bogner,Furnstahl,Hebeler,Nogga,Schwenk.R.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/1229

The3NFatNNLO;usedsofar.

The3NFatNNLO;usedsofar.R.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/1230R.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/1231

The3NFatNNLO;usedsofar.Small?AppsofN3LO3NF:Triton:Skibinskietal.,PRC84,054005(2021).Neutronmatter:Hebeler,Schwenk,andco-workers,arXiv:1206.0025.Notsmall!(?)R.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/1232

The3NFatNNLO;usedsofar.

Small?

The3NFatNNLO;usedsofar.Small?R.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/12

331-loopgraphs:5topologies2PE2PE-1PERingContact-1PEContact-2PE

R.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/1234

The3NFatNNLO;usedsofar.Small?Large?!

R.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/1235

The3NFatNNLO;usedsofar.Small?Large?!3NFcontactsatN4LOGirlanda,Kievsky,Viviani,PRC84,014001(2011)Spin-OrbitForce!

R.Machleidt36Arealistic,investigationalapproach:useΔ-lessskipN3LO3NFthatmayalreadysolvesomeofyourproblems.includeNNLO3NFatN4LOstartwithcontact3NF,useonetermatatime,e.g.spin-orbitR.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/1237…andthenthereIsalsotheΔ-fulltheory…R.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/1238…andthenthereIsalsotheΔ-fulltheory……butwehavenotimeleftforthat.ConclusionsR.MachleidtProg.TheoryofNuclearForcesFB20,Fukuoka,Japan,08/21/1239ThecircleofhistorythatwasopenedbyYukawain1935isclosing.Onemajormilestoneofthepastdecade:“highprecision〞NNpots.atN3LO.Buttherearestillsome“subtleties〞